A167333 Totally multiplicative sequence with a(p) = 2*(5p-1) = 10p-2 for prime p.

1, 18, 28, 324, 48, 504, 68, 5832, 784, 864, 108, 9072, 128, 1224, 1344, 104976, 168, 14112, 188, 15552, 1904, 1944, 228, 163296, 2304, 2304, 21952, 22032, 288, 24192, 308, 1889568, 3024, 3024, 3264, 254016, 368, 3384, 3584, 279936, 408, 34272, 428

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Formula

Multiplicative with a(p^e) = (2*(5p-1))^e. If n = Product p(k)^e(k) then a(n) = Product (2*(5*p(k)-1))^e(k).

a(n) = A061142(n) * A166654(n) = 2^bigomega(n) * A166654(n) = 2^A001222(n) * A166654(n).

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((5*fi[[All, 1]] - 1)^fi[[All, 2]])); Table[a[n]*2^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 06 2016 *)
f[p_, e_] := (10*p-2)^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 18 2023 *)

Prog

(PARI) a(n) = {my(f=factor(n)); for (k=1, #f~, f[k, 1] = 10*f[k, 1]-2; ); factorback(f); } \\ Michel Marcus, Jun 06 2016

Crossrefs

Cf. A001222, A061142, A166654.

Sequence in context: A063840 A180117 A339633 * A259642 A045000 A205871

Adjacent sequences: A167330 A167331 A167332 * A167334 A167335 A167336

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved